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A248141
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Table read by rows: n-th row contains all subsets of consecutive numbers of 1..n.
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3
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1, 1, 2, 1, 2, 1, 2, 3, 1, 2, 2, 3, 1, 2, 3, 1, 2, 3, 4, 1, 2, 2, 3, 3, 4, 1, 2, 3, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 2, 3, 3, 4, 4, 5, 1, 2, 3, 2, 3, 4, 3, 4, 5, 1, 2, 3, 4, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6
(list;
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refs;
listen;
history;
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internal format)
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OFFSET
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1,3
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COMMENTS
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A000292(n) = length of n-th row, whereas A000217(n) = number of all consecutive subsets of numbers 1..n;
A248147(n,k) = A000040(T(n,k)), 1 <= k <= A000292(n).
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LINKS
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Reinhard Zumkeller, Rows n = 1..20 of triangle, flattened
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EXAMPLE
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. 1: 1
. 2: 1,2,1,2
. 3: 1,2,3,1,2,2,3,1,2,3
. 4: 1,2,3,4,1,2,2,3,3,4,1,2,3,2,3,4,1,2,3,4
. 5: 1,2,3,4,5,1,2,2,3,3,4,4,5,1,2,3,2,3,4,3,4,5,1,2,3,4,2,3,4,5,1,2,3,4,5
rows concatenated from:
. 1: [1]
. 2: [1] [2] [1,2]
. 3: [1] [2] [3] [1,2] [2,3] [1,2,3]
. 4: [1] [2] [3] [4] [1,2] [2,3] [3,4] [1,2,3] [2,3,4] [1,2,3,4]
. 5: [1] [2] [3] [4] [5] [1,2] [2,3] [3,4] [4,5] [1,2,3] [2,3,4] ...
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MATHEMATICA
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Flatten[Table[Flatten[Table[Partition[Range[n], i, 1], {i, n}]], {n, 6}]] (* Harvey P. Dale, Feb 03 2015 *)
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PROG
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(Haskell)
import Data.List (group)
a248141 n k = a248141_tabf !! (n-1) !! (k-1)
a248141_row n = a248141_tabf !! (n-1)
a248141_tabf = map concat usss where
usss = iterate f [[1]] where
f vss = group [1 .. last (last vss) + 1] ++
map (\ws -> ws ++ [last ws + 1]) vss
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CROSSREFS
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Cf. A000292 (row lengths), A000217, A248147.
Sequence in context: A105265 A193360 A061394 * A220694 A136314 A121997
Adjacent sequences: A248138 A248139 A248140 * A248142 A248143 A248144
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KEYWORD
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nonn,tabf
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AUTHOR
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Reinhard Zumkeller, Oct 02 2014
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STATUS
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approved
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